Eigenstate structure in many-body bosonic systems: Analysis using random matrices and $q$-Hermite polynomials

TL;DR

This paper investigates the eigenstate structure of many-body bosonic systems using random matrix models and $q$-Hermite polynomials, revealing how centrosymmetry influences quantum transport efficiency.

Contribution

It introduces an analytical framework based on bivariate $q$-Hermite polynomials for understanding eigenstate properties in bosonic systems modeled by BEGOE.

Findings

Centrosymmetry enhances quantum transport efficiency.

Analytical formulas accurately describe eigenstate structure in strong interaction regimes.

Random matrix models effectively capture localization and entropy in many-body bosonic systems.

Abstract

We analyze the structure of eigenstates in many-body bosonic systems by modeling the Hamiltonian of these complex systems using Bosonic Embedded Gaussian Orthogonal Ensembles (BEGOE) defined by a mean-field plus $k$-body random interactions. The quantities employed are the number of principal components (NPC), the localization length ($l_H$) and the entropy production $S(t)$. The numerical results are compared with the analytical formulas obtained using random matrices which are based on bivariate $q$-Hermite polynomials for local density of states $F_k(E|q)$ and the bivariate $q$-Hermite polynomial form for bivariate eigenvalue density $\rho_{biv:q}(E,E_k)$ that are valid in the strong interaction domain. We also compare transport efficiency in many-body bosonic systems using BEGOE in absence and presence of centrosymmetry. It is seen that the centrosymmetry enhances quantum efficiency.